Discard fat from pan, leaving 1 to 2 tablespoons. Add onion to pan and sauté over medium heat for seven minutes, or until golden. Meanwhile, finely chop walnuts with pulsing motion of food processor. Reduce heat under onion pan to low. Stir in flour, then walnuts, and cook over low heat, stirring, for 1 minute. Stir in pomegranate juice and 1/2 cup water, or pomegranate paste and 1 1/2 cups water, and bring to a simmer, stirring.

Add chicken and any juices on plate to pan. Sprinkle chicken with salt and pepper. Cover and cook over low heat about 35 minutes for breast pieces or 40 to 45 minutes for leg and thigh pieces, or until chicken is tender, turning occasionally. Remove chicken from pan. Add tomato paste, if you like, and cardamom to sauce and simmer until thickened to your taste. Taste, adjust seasoning, and add lemon juice and sugar if needed. If you like, whisk in a few more teaspoons pomegranate juice or paste. Return chicken to sauce and heat through.

Serve hot, garnished if you like with pomegranate seeds, parsley or walnuts, or all three.